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CHAPTER 1 to 4 REVIEW Chandrika and Naima

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**Chapter 1: Polynomial Functions**

Function in the form Type of symmetry Odd function/ even function Degrees Domain& range X and y intercept Finite difference End behaviour Transformation in the form Local maximum/ minimum Average rate of change Instantaneous rate of change

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**Q.Find the local minimum of p(x) if**

End Behaviour: II quadrant to I quadrant Zeroes: x=-2 order 1, cross x=-1 order 1, cross x=2 order 2, touch and turn x-intercept: p(0)=8, (8,0) y-intercept: (0,-2) and (0,-1) Local minimum: (8,0) if

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The volume of a balloon is given by where is the time in hour and is volume in cubic inches. Find the average rate of change between t=10 and t=13.

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A water tank draining according to the function where t is the time in hours such that . How fast is the water draining at the end of the 3rd hour? . =-4500unit/h

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**Chapter 2: Polynomial Equations and Inequalities**

Remainder theorem: When a polynomial p(x) is divided by (x-a) the remainder is p(a) Factor theorem: When , (x-a) is a factor of p(x) if p(a)=0. Complex Conjugates: If (a+bi) is a root , that is (x-(a+bi)) is a factor of p(x), then (a-bi) is also a root. If is a root, then is also a root. Rational Zero theorem: If (p,q are integers s.t q does not equal to 0), then (qx-p) is a factor of the polynomial. Family of polynomial functions: Inequalities

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The volume, V, in cubic centimetres, of a block of ice that a sculptor uses to carve the wings of a dragon can be modelled by , where x represents the thickness of the block, in centimetres. What maximum thickness of wings can be carved from a block of ice with volume 2532cm. . Solve the equation Use rational theorem to list factors; Possible values;

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**Cookies are packed in boxes measure 2cm by 8cm by 10cm**

Cookies are packed in boxes measure 2cm by 8cm by 10cm. A larger box is designed by increasing its length, width, and height of the smaller box by same length. Find the possible dimensions of the new box if the volume Is at least . . 12+2=14,12+10=22,12+8=20 Possible dimensions: 6 x 12 x 14 or 14 x 20 x 22 (x cannot be -12)

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**Chapter 3: Rational functions**

Reciprocal of Linear Functions. Review point, jump, infinite discontinuity.

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**Reciprocal of Quadratic Functions**

f(x) g(x)= f(x)<or>0 g(x)<or>0 f(a)=o,f(x) a g(x) undefined f(x) increasing g(x) decreasing f(x)=1 g(x)=1 y-int of f(x) at y=b y-int of g(x) at y=1/b g(x) 0 If f(x) is odd g(x) is odd If f(x) has max or min at (p,q) g(x) has max or min at (p,1/q) f(x) is even g(x) is even

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**Four types reciprocal of quadratic functions**

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**Chapter 4: Trigonometry**

Trigonometric Identities Radian Measure Special angels Proving Identities Different angle formulas (eg. Double angle, half angle, compound angle)

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**Verify that is an identity**

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Special angles

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Identities

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Lesson 3.4 – Zeros of Polynomial Functions Rational Zero Theorem

Lesson 3.4 – Zeros of Polynomial Functions Rational Zero Theorem

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